**Fall Seminar 2017**

- Javier J. Gutiérrez (UB): On triangulated monads and categories of module spectra
18 September 2017, 12:00, IMUB

Abstract: I will report on recent work by Dell'Ambrogio and Sanders where they prove that if we have a monad on an idempotent complete triangulated category such that its Eilenberg-Moore category of modules is also triangulated in the unique compatible way, then any other triangulated adjunction realizing this monad is "essentially monadic". As an application, one can obtain that, in the stable homotopy category of spectra, the category of homotopy modules is triangulated if and only if it is equivalent to the homotopy category of strict modules.

- Joana Cirici (Münster): Sheaves of
*E*-infinity algebras and applications to algebraic geometry2 October 2017, 12:00, IMUB

Abstract: I will give a sheaf-theoretic description of the

*E*-infinity structure carried by the singular cochain complex of every reasonable topological space. I will then discuss some applications to the study of Steenrod operations associated with algebraic varieties. This is joint work in progress with David Chataur. - Federico Cantero (BGSMath-UB): Homotopy type of spaces of submanifolds I
16 October 2017, 12:30, IMUB

Abstract: In this talk I will explain how to deform certain spaces of submanifolds to smaller subspaces, whose homotopy type can be calculated.

- Federico Cantero (BGSMath-UB): Homotopy type of spaces of submanifolds II
30 October 2017, 12:30, IMUB

- Carles Casacuberta (UB): Recollements
13 November 2017, 12:30, IMUB

Abstract: Suppose given a spectrum

*E*such that the class of*E*-null spectra is also the class of*H*-acyclic spectra for some homology theory*H*. Then*E*-nullification and*H*-acyclization together with*H*-localization and*E*-cellularization fit into a*recollement*. In this talk we will describe recollements in triangulated categories and discuss the special case of the sphere spectrum in motivic homotopy. - Javier J. Gutiérrez (UB): Morita homotopy theory for (∞, 1)-categories
27 November 2017, 12:30, IMUB

Abstract: In this talk, we will discuss the existence of Morita model structures on the categories of small simplicial categories and simplicial sets, modelling the Morita homotopy theory of (∞, 1)-categories. The weak equivalences of these model structures can be characterized in terms of simplicial presheaves and slice categories, respectively. Finally, we will show that the Morita model structure for simplicial categories can also be obtained as an explicit left Bousfield localization of the Bergner model structure on simplicial categories.

- Federico Cantero (BGSMath-UB): Surface bundles over surfaces with arbitrarily many fiberings
18 December 2017, 12:30, IMUB

Abstract: In this talk I will give an exposition of the paper of the same title by Nick Salter. We will construct examples of 4-manifolds that can be realised as total spaces of different surface bundles over surfaces.

- Joana Cirici (UB): Galois actions, purity and formality
29 January 2018, 12:00, IMUB

Abstract: I will explain how to use the theory of weights on étale cohomology to study formality with torsion coefficients, for certain schemes defined over a finite field. As an application, I will give some partial results of formality for the differential graded algebra of singular cochains with torsion coefficients of certain configuration spaces. This is joint work in progress with Geoffroy Horel. In fact, it is a sequel of our previous work on formality with rational coefficients, reported last spring by Geoffroy at the UB's Topology Seminar.